摘要

在圖像科學和自由邊界問題中所產生的一個新方法是數學應用的一個很好的例子。這個方法就是由Osher和Sethian在1987年提出的用於獲取運動邊線的水準集合方法。它是一種非常成功的數值方法技術，如果我們在google上輸入“水準集合”然後進行搜索，就會有190,000個查詢結果。它的應用從獲取多相動態流到好萊塢所需要的特殊的圖像視覺效果處理，控制，外延生長，電腦視覺以及其他很多方面。在這次講座中，我們主要回顧一下數值方法技術及其與基於圖像科學和應用的PDE領域的關係。圖像分析是現實世界中的例子，而電腦圖形則是虛擬世界中的例子。

Abstract

A good example of the applications of mathematics involves a new approach to image science and free boundary problems in nature. This is exemplified by the level set method for capturing moving fronts, which was introduced in 1987 by Osher and Sethian. It has proven to be phenomenally successful as a numerical device. For example, typing in "Level Set Methods" on google's search engine gives roughly 190,000 responses. Applications range from capturing multiphase fluid dynamical flows, to special effects in Hollywood to visualization,image processing, control, epitaxial growth, computer vision and many more. In this talk we shall give a quick overview of the numerical technology, its relation with the field of PDE based imaging science and some application. The real world is exemplified by image analysis and the fake world is exemplified by computer graphics.